[1] Deformation of till produces power law creep for low strain at stresses high enough to cause permanent deformation but below the shear strength. Experiments were conducted on till (a mixed size granular material) from Matanuska Glacier, Alaska, and the Scioto (Ohio) Lobe of the Laurentide Ice Sheet (Caesar till). We deformed till in double direct shear under fixed shear velocity or shear stress (creep). Normal stress ranged from 50 kPa to 5 MPa at shearing rates ranging from 1 to 300 mm/s for 1 cm thick samples. Creep was induced via small step perturbations in stress. Fabric development within till layers was investigated by varying shear strain prior to creep tests. In velocitycontrolled experiments, till deforms as a nearly Coulomb plastic material with slight velocity strengthening, corresponding to a stress exponent, n > 60. Creep experiments conducted well below the shear strength indicate lower n values, increasing as shear stress increases. With increasing initial strain and inferred fabric development, the creep strain rate decreases while n increases. Experiments at a normal stress of 1 MPa and no initial strain show n = 6.8, increasing to n = 17.5 at higher shear strains; however, strain rate was still decreasing and thus these values represent maximum estimates. Our data show that in the absence of dilatant hardening till exhibits rate sensitivity at strain of order 1 or less. At low strains, n likely depends on consolidation state, permeability, and dilation. Deformation is nearly rate insensitive (Coulomb plastic) at shear stress near the shear strength or at high strain.

[1] We performed laboratory experiments to investigate shear localization and the evolution of frictional behavior as a function of shear strain. Experiments were conducted on water-saturated layers, 0.3-1 cm thick, of Caesar till, a granular material analogous to fault gouge. We used the double-direct shear configuration at normal stresses ranging from 0.5 to 5 MPa and shearing velocities of 10-100 mm/s. Shear localization was assessed via strain markers and two proxies: (1) macroscopic layer dilation in response to perturbations in shear stress and (2) rate/state friction response to shear velocity perturbations. In creep mode experiments, at constant shear stress, we monitored dilation for perturbations in shear stress. In standard friction tests, we measured the coefficient of friction during perturbations in macroscopic strain rate. We find evidence of strain localization beginning at shear strain g % 0.15 and continuing until g % 1. Analysis of strain markers supports interpretations based on the proxies for localization and shows that strain is localized in zones of finite thickness. We also investigate symmetry of the friction response to step changes in imposed slip velocity and find that the behavior is symmetric. Our results favor the Ruina law for friction state evolution in which slip is the fundamental variable rather than the Dieterich law. The critical slip distance for friction evolution, D c , is $140 mm. The Dieterich state evolution law requires different values of D c for velocity increases/decreases, 100 mm versus 175 mm, respectively, and would imply strain localization/delocalization associated with shear in a finite zone.Citation: Rathbun, A. P., and C. Marone (2010), Effect of strain localization on frictional behavior of sheared granular materials,

[1] We performed laboratory experiments to investigate the processes responsible for rate and state friction (RSF) behavior in fault rocks. We focused on the symmetry of the frictional constitutive response to velocity changes and the mechanics of the critical friction slip distance D c . Experiments were conducted in double direct shear at 1 and 25 MPa normal stress, at room temperature, and for shearing velocity from 1 to 300 mm/s. We studied three granular materials and bare surfaces of Westerly granite. Ruina's law, which predicts frictional symmetry between velocity increases and decreases, better matches our data than Dieterich's law, which predicts that velocity decreases should evolve to steady state at a smaller displacement. However, for granular shear, in some cases D c is smaller for velocity increases than for velocity decreases, contrary to expectations from either law. On bare granite surfaces, the frictional response is symmetric for velocity increases/decreases. Two distinct length scales for D c and two-state variables are required for granular shear in some cases. We hypothesize that asymmetry and two-state behavior are caused by shear localization and changes in shear fabric in fault gouge. Our measurements show that during steady state frictional shear, dilation after a velocity increase is smaller than compaction after a decrease. Normal stress oscillations cause a marked decrease in D c . Reduction of D c reduces frictional stability, enhancing the possibility of seismic slip. Our experiments show that shear localization and fabric within the fault gouge can influence the RSF parameters that dictate earthquake nucleation and dynamic rupture.Citation: Rathbun, A. P., and C. Marone (2013), Symmetry and the critical slip distance in rate and state friction laws,